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Weierstrass; Sonja Kowalewski

YOUNG doctors in mathematics, anxiously seeking positions in
which their training and talents may have some play, often ask
whether it is possible for a man to do elementary teaching for
long and keep alive mathematically. It is* The life of Boole is a
partial answer; the career of Weierstrass, the prince of analysts,
the father of modern analysis', is conclusive.
Before considering Weierstrass in some detail, we place him
chronologically with respect to those of his German contem-
poraries, each of whom, like Mm, gave at least one vast empire
of mathematics a new outlook during the second half of the
nineteenth century and the first three decades of the twentieth.
The year 1855, which marks the death of Gauss and the break-
ing of the last link with the outstanding mathematicians of the
preceding century, may be taken as a convenient point of refer-
ence. In 1855 Weierstrass (1815-97) was forty; Kronecker
(1S2S-91), thirty-two; Riemann (1826-66), twenty-nine; Dede-
kind (1831-1916), twenty-four; while Cantor (1845-1918) was
a small boy of ten. Thus German mathematics did not lack
recruits to carry on the great tradition of Gauss. Weierstrass
was just gaining recognition; Kronecker was well started; some
of Riemann's greatest work was already behind him, and
Dedekind was entering the field (the theory of numbers) in
which he was to gain his greatest fame. Cantor, of course, had
not yet been heard from.
We have juxtaposed these names and dates because four of
the men mentioned, dissimilar and totally unrelated as much of
their finest work was, came together on one of the central
problems of all mathematics, that of irrational numbers:
Weierstrass aod Dedekind resumed the discussion of irrationals